Can you stop a sun lamp from lighting specific objects in a scene?
If your problem is unwanted light in certain areas of the scene.. or to reduce the overall lighting in an area and make a bit dark, Blender really has an awesome way to do that. So, let me explain with an example here:
Consider this scene where I want to reduce the effect of light in the area below the monkey face on the background code structure. Lets say I want to make it darker and remove some light. Here is the actual scene if u use just the overall sun.

Now, I have added a area light in the required area. Interestingly you can make the values of light in &quot;Negative&quot; numbers. Yeah!! That means you can start to remove the light in that area and below is the example of the same. You can adjust the value of it as required to create the required effect!

This way you can affect certain areas in scene to be not light up and if you want to wholly remove light effect on a singular object, you can try the other answer
as mentioned above. Hope this helps you in your scene.